Decaying Majoron DM and Structure Formation kingman Cheung - - PowerPoint PPT Presentation

Decaying Majoron DM

and

Structure Formation

kingman Cheung September 11 2019 TAUP

References

Majoron DM: Berezinsky and Valle, PLB318 (1993), 360 CMB constraint: Lattanzi, Riemer-Sørensen, Tortola, Valle, 
 PRD 88 (2013) 063528 Structure Formation: Kuo, Lattanzi, KC, Valle, JCAP 1812 
 (2018) 12


Lambda Cold Dark Matter Model

❖ Standard model of Cosmology.

Dark matter consists of unknown elementary particle(s), produced in early universe, that is “cold” — velocity dispersion on structure formation is negligible. 


❖ Explains structure formation for large scales: 


with small density fluctuations normalised to the observed CMB and allowed 
 to grow via gravitational instability, can account for many properties of structures a
 t most well- observed scales and epochs. On scales larger than about 10 kpc, 
 the predictions of ΛCDM have been successful. 


Yet, for scale smaller than 10 kpc, inconsistent with observations.


Missing satellite problem, the too-big-to-fail problem, the cusp-core problem.


Cusp-Core Problem

❖ LCDM simulations predict DM

density cusp in center of galaxies, but inconsistent with

• bservations.

❖ Especially low-mass galaxies.

A Few Possible Solutions

❖ Baryon physics: efficiency of transforming baryons into stars to be

lower in lower-mass systems.

❖ Some warm DM: its thermal velocity dispersion provides free streaming

that suppresses low-mass halos or sub-halos, and also reduce the density cusp at the center.

❖ DM has self-interactions, reducing the density cusp, form less sub-

halos.

❖ Fuzzy dark matter: large de Broglie wavelength suppresses 


small-scale structures (Hu et al.).

Outline

• 1. Warm DM with relativistic properties can alleviate 


the small-scale crisis. Majoron DM is warm.


• 2. In addition, majoron DM can decay into neutrinos:


with a life-time of order of the age of the Universe.
 


• 3. CMB provides a strong constraint on majoron DM 


life-time, in order to avoid producing too much 
 fluctuation power on the largest CMB scales.


• 4. We investigate the WARM and DECAY nature of


majoron DM on structure formation. J → νν

Majoron Physics

The seesaw mechanism involves spontaneously broken
 lepton number symmetry, involves a singlet scalar 
 coupling to singlet neutrino:

λσνcT

L τ2νc L,

⟨σ⟩ ≡ v1

v1 can be large to give a large majorana mass. So the mass
 matrix for left- and right-handed neutrino is

M ¼ Y3v3 Yv2 YTv2 Y1v1 " #

mν = Y3v3 − YνY−1

1 YT ν

v2

2

v1

v3 (v2) is the VEV of the Higgs triplet (doublet).
 Since the lepton-number symmetry is spontaneously
 broken, there is Nambu-Goldstone boson:

J ∝ v3v2

2ℑ(Δ0) − 2v2v2 3ℑ(Φ0) + v1(v2 2 + 4v2 3)ℑ(σ)

In principle, J is massless but acquires a mass via non-
 perturbative gravitational effect.

mJ ≃ O(keV)

J mainly decays into light neutrinos via

ℒY = i 2 J ∑

ij

νT

i gijτ2νj + h . c .

gij = − mνi v1 δij Decay width into neutrinos is

ΓJ→νν = mJ 32π ∑i m2

νi

2v2

1

Subleading decay into a pair of photons: ΓJ→γγ = α2m3

J

64π3 ∑

f

NfQ2

f

2v2

3

v2

2v1

(−2Tf

3) m2 J

12m2

f 2

Structure Formation

We examine the effect of decaying warm dark matter on non-linear structure formation, due to two effects (1) Warm nature (free streaming) of the majoron DM (2) Decay of majoron DM

Goal of this study

Abbreviations Initial Conditions Lifetime WDM mass SCDM CDM ∞ N/A DCDM CDM 50 Gyr N/A SWDM-M WDM ∞ 1.5 keV DWDM-M WDM 50 Gyr 1.5 keV SWDM-m WDM ∞ 0.158 keV DWDM-m WDM 50 Gyr 0.158 keV

Table 1. The abbreviations and features of the simulations we have performed in this article. To avoid word cluttering in the following we will use these abbreviations.

We use two values for mJ = 0.158 eV and 1.5 eV and lifetime

• The lighter one is for thermal DM production

• the heavier one is for non-thermal history or based
• n thermal production but later diluted by additional

entropy after decoupling.

• The lifetime from CMB constraint is 50 Gyr. We 


also study the stable DM case. τ = 50 Gyr or ∞

Remarks:

• The lighter mass 0.158 keV gives the correct relic


density as a scalar particle that decouples in early


• Universe. 

• Both values are in tension with the lower limit from


Lyman-alpha, mJ > 3.5 keV . Nevertheless, the limit is
 model dependent, e.g., IGM thermal history.


• If mJ = 5.3 keV is chosen, it is almost no different from CDM.

• The lighter value is chosen so as to maximize the 


free streaming effects. And it mainly decays into neutrinos.


• Here we only investigate the effects of free streaming and 


decays, not the exact mass limit from structure formation.

Simulation of Decaying particle

• We concern with decay of DM into relativistic neutrinos
• The mass of “simulation particles” is reduced by a small


amount at each time step due to decay of DM:

M(t) = M(1 − R + R e−t(z)/τJ), mass of the simulation particles , and

where R ≡ (ΩM − Ωb)/ΩM is the DM fraction

• In addition to reducing simulation particle mass,


the expansion rate of the Universe also modified
 according to the energy content at each z

The evolution of DM and decay product is described by

˙ ρdm + 3Hρdm = − a τJ ρdm, ˙ ρdp + 4Hρdp = a τJ ρdm,

H and a are the conformal Hubble parameter and scale factor.
 The Hubble parameter at each red-shift is

H H2(z) = 8πG 3 a2(ρdm(z) + ρb(z) + ρdp(z) + ρΛ(z)),

• are unaffected by energy exchange between DM and dp, so


they evolve in standard way:

ρb , ρΛ

ρb ∝ a−3, ρΛ ∝ const

• Further assumption: contribution of decay product dp to energy 


density is very small, due to long lifetime of majoron.


• The decay product, neutrinos, are free streaming and do not cluster.

• The decay is to reduce the amount of matter that is able to cluster. 


But we expect this assumption to break down on the largest scale 
 above the free-streaming length, which is the size of horizon scale
 much larger than our simulation size. 


• Given initial conditions for we solve for the evolution equations


and calculate the Hubble parameter at each time-step ρdm , ρdp

Initial Conditions

❖ Use linear theory to evolve the primordial perturbation

in k space to some initial redshift z = 99, which is well before the DM decays, so decaying DM and stable DM have the same initial condition.


❖ In WDM, we estimate the initial power spectrum as



 
 
 where transfer function TWDM(k)

PWDM(k) = T 2

WDM(k) × PCDM(k) ,

TWDM(k) =

• 1 + (αk)2ν5/ν ,
• where α = 0.048(ΩDM/0.4)0.15(h/0.65)1.3(keV/mDM)1.15(1.5/g)0.29 Mpc and ν = 1.2.

Ω is the dark matter energy density, m ⌘ m is the dark matter mass and g is

Initial matter power spectra for CDM and WDM using 2LTPic code.
 Power spectrum drops to 1/ e of CDM at k≈1 (0.158 keV) and 
 17h (1.5 keV). These are roughly the free-streaming wave numbers.

Simulation Details


• starts at z = 99
• both stable and decaying DM exact same initial 


conditions and same random seed.

• For WDM simulations, thermal velocity at z=99 was input


to simulation particles consistent with initial spectrum.

• Other cosmological parameters:

Ωm = 0.3, ΩΛ = 0.7, Ωb = 0.04; h = 0.7, ns = 0.96, σ8 = 0.8

• Use 5123 simulation particles in a cube with side 50 h-1 Mpc
• Msim ≈ 7

.8 107 h-1 Msun.

• Periodic boundary condition.

Density Fields

Simulation Results

Density field: 1 + δ = ρ/ ¯ ρ M: 1.5 keV , m: 0.158 keV

Stable / Decay log10(ρS/ρD) = log10[(δS + 1)exp(t0/τJ)] − log10(δD + 1)

Matter Power Spectrum

Matter Power Spectrum comparison

Interpretations

• Effects of decay is more obvious at low z
• Compare SCDM with SWDM-(M,m), at large scale (small k)


are very close, but differ at small scale (large k), due to 
 free-streaming of WDM.

• Free-streaming of mJ=1.5 keV is really small.
• Compare DWDM-M and DWDM-m, free-streaming effect still


there for small scale suppression.

• Further suppression at all scales due to decay, which do not


show strong dependence on scales. In contrast to free-
 streaming effect of WDM.

Ratio of matter power spectrum

• The decay suppresses the matter power at all scales.
• The suppression due to decay is more obvious at small scale.
• The suppression due to decay gradually decreases toward 


large scale. All curves converge to the same value as beyond
 free-streaming length CDM and WDM behave the same.

• Nonlinear enhancement of the effect of decay on small scales


is stronger for lighter WDM. There is a sharp drop for 
 mJ=0.158 keV near the free-streaming length scale.

Halo Mass Function

Remarks from Halo mass functions

• Compare stable and decaying DM, the decay reduced the 


number density of halos at all mass scales.


• Free-streaming effect of WDM is to set a cutoff halo mass,


where the WDM halo mass function starts to deviate from 
 CDM halo mass function.


• At large halo masses, the difference among various cosmo-


logies are difficult due to few halos with large mass.


• Number density of small-mass halos is much higher in CDM 


than WDM

n(M) = (1 + Mhm/M)−γ × nTinker(M) Halo mass function fit: γ ≈ 0.309 γ ≈ 0.345 (SWDM-m) (DWDM-m)

Deviations in WDM due to many spurious halos (numerical artifacts) due to strong cutoff in WDM transfer fuction

Outlooks and Further Improvements

Include baryons in simulations — ability to cool down by 
 radiative processes, gravitational heated, affects the halo
 density profile, star formation, other compact massive objects.
 Here we ignore the free-streaming effects of the neutrinos.
 If the decay time is much shorter (but much later than CMB),
 relativistic effect is important in large scales.
 Other scenarios: * CDM decays into relativistic neutrinos, * CDM decays into another CDM, velocity boost, * CDM interacts non-trivially with baryons, non-minimal heat
 exchange between CDM and baryons.


Back up Slides

Check for mJ=5.3 keV

Numerical Convergence tests

There are two numerical limitations:

• cosmic variance — finite volume of simulations, preventing


predictions at very large scale. Box size:
 50 h-1 Mpc, corresponding to k≈0.13 h Mpc-1.


• Discreteness of simulation particles

• Resolution limited by box size and the number of particles,


described by Nyquist wavenumber
 Beyond that the accuracy strongly degraded.

KNyq = π(N/V)1/3 ≃ 32 h Mpc−1

Consequences of finite resolution

• Non-zero power exists on all scales — shot noise. 


Independent of k, but depend on the number of 
 simulation particles.

• A discrete peak in power spectrum at 2 x Nyquist limit.

The excess power is of more problem to WDM because

• f much small power at small scales — well known

spurious halo issue in WDM simulations We compare simulations at z=0 with different N and V

N = 1283, 2563, 5123; L = V1/3 = 50,100 h−1 Mpc

In almost entire range of scales the matter power spectrum
 at different resolution converge all the way up to Nyquist limit.

Ratio of power spectrum for L = 50 and 100 h-1 Mpc.
 The green band is 10% deviation.

Ratio of matter power spectrum at z = 0

CMB Constraint

J → νν

Lattanzi, Riemer-Sorense, Tortola, Valle 2013

2 4 6 8 10 0.07 0.08 0.09 0.1 0.11 0.12

J

10 19s 1

DMh2

2 4 6 8 10 0.14 0.15 0.16 0.17 0.18

J

10 19s 1 mJ

eff keV

ΓJ→νν ≤ 6.4 × 10−19 s−1

at 95 % CL

meff

J

= 0.158 ± 0.007 keV

Late DM decay to invisible relativistic particles:

• gives extra radiation at small redshifts
• too much power to CMB at the large angular scale.

Thus, CMB can constrain the decay rate or lifetime of J.

X-ray, Gamma-ray Constraint

J → γγ

Lattanzi, Riemer-Sorense, Tortola, Valle 2013

3-sigma line emission constraint on DM -> 2 photons The most relevant
 range for majoron by: Chandra LETG XMM M31 and MW

Lattanzi, Riemer-Sorense, Tortola, Valle 2013

Model predictions with various v3